Confinement-Higgs and deconfinement-Higgs transitions in four-dimensional SU(2) LGT at finite temperature

TL;DR

The paper addresses the finite-temperature phase structure of the (3+1)-D SU(2) lattice gauge–Higgs theory with fundamental Higgs fields. It implements two non-local order parameters—the Greensite–Matsuyama overlap, with realizations $G_{1s}$ and $G_w$, and the Fredenhagen–Marcu operator $\rho = \lim_{R\to\infty} H(R,T)$—via Monte Carlo simulations on Nt$=4$ lattices across the $(β,γ)$ plane. The main findings show that the overlap operators vanish in the confinement and deconfined phases and remain nonzero in the Higgs phase, producing a β-dependent critical band; FM operators tend to nonzero constants in confinement/Higgs and decay toward zero with distance in the deconfined regime, though large errors limit definitive conclusions. The work demonstrates that non-local order parameters can diagnose finite-temperature phases in gauge–Higgs systems, while highlighting the need for larger volumes and improved statistics to sharpen phase boundaries.

Abstract

We re-examine by numerical simulation the phase structure of the (3+1)-dimensional SU(2) lattice gauge theory (LGT) with gauge fields coupled to Higgs fields at finite temperature. Concretely, we explore two different order parameters which are able to distinguish the three phases of the theory: (i) the Fredenhagen-Marcu operator used to discriminate between deconfinement and confinement/Higgs phases and (ii) the Greensite-Matsuyama overlap operator proposed recently to distinguish confinement and Higgs phases.

Figures (9)

• Figure 1: Phase diagram of the $SU(2)$ gauge-Higgs theory on the lattice at finite temperature in the $(\beta,\gamma)$-plane for $N_t=4$. See text for details.
• Figure 2: Overlap operators at $\beta=2.6$, $N_t=4$, $L=16$.
• Figure 3: Overlap operators at $\beta=2.0$, $N_t=4$, $L=16$.
• Figure 4: Overlap operators at $\beta=1.0$, $N_t=4$, $L=16$.
• Figure 5: Overlap operators at $\beta=2.6$, $N_t=4$.